Two systems of inequalities to be solved at the same time are just one system consisting of all the inequalities from the two systems.
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celtschkOct 20 '12 at 7:32

Because each of $A$ and $B$ is relatively closed in $A\cup B$ and $A\cup B$ is connected, the only possible solutions would be when either $A$ or $B$ is empty. (It would be interesting to find ways to get Mathematica to perform such forms of topological reasoning.)
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whuberOct 20 '12 at 17:21

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